WEBVTT Kind: captions; Language: en 00:00:26.001 --> 00:00:29.001 Man has described himself in many ways. 00:00:30.000 --> 00:00:35.001 But if we concentrate on man in relation to his control over his environment, no 00:00:35.001 --> 00:00:41.000 description is more apt than the description of man as a tool-making animal. 00:00:44.000 --> 00:00:48.001 And in the short history of mankind, the majority of the tools which man is made 00:00:48.001 --> 00:00:54.000 can be thought of as an extension of his muscle power, that is, the ability to 00:00:54.000 --> 00:00:57.000 perform work faster and in greater quantity. 00:01:01.000 --> 00:01:07.001 However, in the mid 00:01:07.001 --> 00:01:13.001 -1940s and the 20th century, a different kind of tool was invented, a tool for 00:01:13.001 --> 00:01:16.001 extending certain of the powers of man's mind. 00:01:17.001 --> 00:01:20.001 This tool is the electronic computer. 00:01:53.001 --> 00:01:59.001 It is the fast, reliable, and tireless performance of a variety of arithmetic and 00:01:59.001 --> 00:02:04.000 logical operations that gives the computer its great utility and power. 00:02:04.001 --> 00:02:08.000 But merely looking at a computer won't tell us very much about 00:02:08.000 --> 00:02:09.001 what it actually is doing. 00:02:10.000 --> 00:02:14.000 Neither will this tell us anything about the revolutionary material and 00:02:14.000 --> 00:02:16.000 intellectual effects of such machines. 00:02:17.000 --> 00:02:20.001 We can easily see the material and intellectual effects of, 00:02:20.001 --> 00:02:22.000 say, machines for transportation. 00:02:23.001 --> 00:02:30.000 We know that the modern jet aircraft represents a great increase in 00:02:30.000 --> 00:02:31.001 speed over the earliest aircraft. 00:02:32.000 --> 00:02:37.000 We also know that modern airplanes have made the world smaller and changed our 00:02:37.000 --> 00:02:40.000 way of thinking about ourselves and our world. 00:02:41.000 --> 00:02:44.001 And future means of transportation will bring even more 00:02:44.001 --> 00:02:46.001 rapid and radical changes. 00:02:48.000 --> 00:02:53.000 But even the difference between the speed of an ox cart and the fastest rocket is 00:02:53.000 --> 00:02:58.001 small when compared with the difference in speed between calculation by hand 00:02:58.001 --> 00:03:00.001 and calculation by computer. 00:03:02.000 --> 00:03:06.001 For example, the first electronic calculator to be completed could do the work of 00:03:06.001 --> 00:03:09.001 50,000 people working by hand. 00:03:12.000 --> 00:03:17.000 Scientists, when they speak of a great change in speed or size, prefer to speak 00:03:17.000 --> 00:03:22.000 in terms of a unit of measurement called an order of magnitude, meaning 00:03:22.000 --> 00:03:23.001 ten times as much. 00:03:25.000 --> 00:03:28.000 Dr. Richard Hamming, a research mathematician for the Bell Telephone 00:03:28.000 --> 00:03:32.001 Laboratories, in a paper presented before a meeting of the American Academy for 00:03:32.001 --> 00:03:35.000 the Advancement of Science, put it this way. 00:03:35.000 --> 00:03:38.000 The computer revolution is often compared with the famous industrial 00:03:38.000 --> 00:03:40.000 revolution in importance and scope. 00:03:41.000 --> 00:03:44.000 The industrial revolution effectively freed man from being a beast of burden. 00:03:44.001 --> 00:03:48.000 The computer revolution will similarly free him from dull, repetitive routine. 00:03:49.000 --> 00:03:53.000 The computer revolution is, however, perhaps better compared with the Copernican 00:03:53.000 --> 00:03:57.001 or the Darwinian revolution, both of which greatly change man's idea 00:03:57.001 --> 00:03:59.000 of himself and the world in which he lives. 00:04:00.000 --> 00:04:03.000 Before getting into the main part of this paper, it is necessary to discuss 00:04:03.000 --> 00:04:06.000 briefly the idea of a change in a technology. 00:04:07.000 --> 00:04:11.000 Change is often measured in units of an order of magnitude, meaning roughly a 00:04:11.000 --> 00:04:13.000 factor of ten, ten times as much. 00:04:14.000 --> 00:04:17.001 It is a common observation that a change of an order of magnitude in a technology 00:04:17.001 --> 00:04:19.001 produces fundamentally new effects. 00:04:20.000 --> 00:04:22.001 As an illustration, consider the following example. 00:04:23.001 --> 00:04:26.000 Modern jet planes are about one order of magnitude 00:04:26.000 --> 00:04:28.000 faster than Wright Brothers' first plane. 00:04:29.000 --> 00:04:32.001 Another example? The fastest missiles are somewhat more than two orders of 00:04:32.001 --> 00:04:35.001 magnitude faster, meaning about three times, three hundred times faster. 00:04:37.000 --> 00:04:39.000 Automobiles are used at speeds around one order 00:04:39.000 --> 00:04:40.001 of magnitude faster than a horse and wagon. 00:04:42.000 --> 00:04:44.000 Each of these have produced whole new effects. 00:04:45.000 --> 00:04:48.000 Indeed, it is said that the automobile has produced even a change in our morals. 00:04:50.001 --> 00:04:53.001 Computers have improved in speed by at least six orders of 00:04:53.001 --> 00:04:55.001 magnitude, a million-fold. 00:04:56.000 --> 00:04:58.001 In order to understand the factor of a million, 00:04:58.001 --> 00:05:00.001 consider the following two situations. 00:05:01.001 --> 00:05:04.000 First, that you have only one dollar, and 00:05:04.000 --> 00:05:05.001 second, that you have a million dollars. 00:05:06.001 --> 00:05:10.000 You can readily see that in the two situations there are 00:05:10.000 --> 00:05:11.001 fundamentally different effects. 00:05:12.001 --> 00:05:15.001 You adopt a different view of yourself and the world in which you live. 00:05:17.000 --> 00:05:20.000 Along with the change in speed, there has been a great increase in reliability, 00:05:20.000 --> 00:05:23.001 so we now do much longer computations than was practical by hand. 00:05:24.001 --> 00:05:28.000 Finally, with the increase in speed, there has been a corresponding decrease in 00:05:28.000 --> 00:05:32.000 the cost, something more than 1,000 times cheaper. 00:05:33.000 --> 00:05:38.000 It is as if suddenly automobiles cost two to four dollars, houses 20 to 60 00:05:38.000 --> 00:05:42.000 dollars, and the changes in the computer technology are still going on. 00:05:43.000 --> 00:05:44.000 These then are the... 00:05:44.000 --> 00:05:47.000 We hardly need to be reminded that we live in a world that is becoming more 00:05:47.000 --> 00:05:50.000 complicated and more crammed with information every day. 00:05:50.001 --> 00:05:54.001 One description for this vast quantity of data on everything from the lifetime 00:05:54.001 --> 00:05:59.000 earning records of an individual to the beeps and pulses relayed to Earth from a 00:05:59.000 --> 00:06:03.000 space satellite uses that overworked word, explosion. 00:06:03.001 --> 00:06:06.000 This time, an information explosion. 00:06:07.000 --> 00:06:12.000 The computer is an invaluable tool for processing these millions of bits of 00:06:12.000 --> 00:06:17.000 information in accurate, fast, and economical fashion, in accordance with rules 00:06:17.000 --> 00:06:20.000 and instructions provided by the human program. 00:06:22.000 --> 00:06:27.000 In the most gigantic of all record-keeping jobs, the social security system, more 00:06:27.000 --> 00:06:30.001 than one million personal records can be processed in one day. 00:06:32.000 --> 00:06:36.001 This manufacturing plant is entirely computer controlled, in accordance with 00:06:36.001 --> 00:06:39.001 rules for decision making stored in the machine's memory. 00:06:43.001 --> 00:06:48.000 This chemical plant for making polyisoprene was designed by a computer. 00:06:49.000 --> 00:06:54.001 In a recent example, a computer in 16 hours and out of 16,000 possible designs 00:06:54.001 --> 00:06:58.001 selected the design that most closely approached the ideal design 00:06:58.001 --> 00:07:00.000 as defined by the engineers. 00:07:09.001 --> 00:07:15.000 This actual firing of the multimillion dollar Saturn rocket was simulated on this 00:07:15.000 --> 00:07:19.000 computer many times before the actual firing was authorized. 00:07:19.001 --> 00:07:23.000 And these simulated firings which helped eliminate many of the problems in the 00:07:23.000 --> 00:07:27.001 functioning of the rocket cost only a fraction of what an actual 00:07:27.001 --> 00:07:29.000 launching would have cost. 00:07:29.001 --> 00:07:36.000 Each of these operations, record-keeping and accounting, control, 00:07:37.000 --> 00:07:43.001 design, and simulation, is achieved through the manipulation of numbers 00:07:43.001 --> 00:07:47.001 according to instructions and rules given to the computer by the programmer. 00:07:48.001 --> 00:07:52.001 But what are these rules and what is the relationship between numbers and the 00:07:52.001 --> 00:07:55.000 real things they are said to represent? 00:07:55.001 --> 00:07:59.001 These are some of the questions that we put to the scientists and we've already 00:07:59.001 --> 00:08:02.001 seen Dr. Richard Hemming, research mathematician 00:08:02.001 --> 00:08:04.001 at the Bell Telephone Laboratories. 00:08:05.000 --> 00:08:10.000 Well, I would say that at the Bell Telephone Laboratories, we do about 10% of the 00:08:10.000 --> 00:08:12.001 experiments on a computer and about 90% in the laboratory. 00:08:13.000 --> 00:08:17.001 I would expect that in time, we will do 90% on the computer and 10% in the lab. 00:08:18.001 --> 00:08:23.001 Speed, cost, and effort favor the computer over the laboratory approach. 00:08:26.000 --> 00:08:29.001 This advantage is possible because we construct a mathematical 00:08:29.001 --> 00:08:31.001 model rather than a material model. 00:08:31.001 --> 00:08:35.000 I use the word construct because the mathematical equations are the construction 00:08:35.000 --> 00:08:38.000 rather than a materialistic physical model. 00:08:39.001 --> 00:08:43.000 It is perhaps fortunate that we have found, particularly in the field of physical 00:08:43.000 --> 00:08:47.001 sciences, that our predictions based upon the mathematical models agree very well 00:08:47.001 --> 00:08:49.000 with what we observe in the physical world. 00:08:49.001 --> 00:08:53.000 The 19th century physicist Heinrich Hertz described the 00:08:53.000 --> 00:08:55.000 concept of a model in these words. 00:08:56.000 --> 00:09:01.001 We make for ourselves internal pictures or symbols of external objects. 00:09:02.000 --> 00:09:06.001 We make them of such a kind that the necessary consequences in thought of the 00:09:06.001 --> 00:09:11.001 internal pictures are always pictures of the necessary consequences in nature 00:09:11.001 --> 00:09:13.001 of the objects symbolized. 00:09:14.000 --> 00:09:17.001 The idea of a mathematical model is fairly easy to understand. 00:09:17.001 --> 00:09:23.001 A very simple, trivial example is the numbers you calculate on your check stubs. 00:09:24.000 --> 00:09:28.000 You combine various numbers by addition, subtraction, and they correspond in a 00:09:28.000 --> 00:09:31.000 very real sense to the amount of money that you have in the bank. 00:09:31.001 --> 00:09:34.000 The mathematical model is the number you manipulate. 00:09:34.001 --> 00:09:37.001 The amount of money you actually have in the bank is the physical world. 00:09:39.000 --> 00:09:42.000 Let us consider now a slightly more complex example. 00:09:44.000 --> 00:09:47.001 This is a common experience for most of us. 00:09:48.000 --> 00:09:51.001 The front end of the car dips sharply when we come to a sudden stop. 00:09:52.000 --> 00:09:57.000 In technical language, there is a transfer of weight from rear to 00:09:57.000 --> 00:09:59.000 front in the action of braking. 00:10:00.000 --> 00:10:04.000 A mathematical model of this transfer of weight can reveal exactly how much 00:10:04.000 --> 00:10:06.000 weight is on both wheels. 00:10:07.000 --> 00:10:10.001 And different road surfaces and braking conditions will result 00:10:10.001 --> 00:10:12.000 in different weight distributions. 00:10:12.001 --> 00:10:16.000 But the mathematical model for the transfer of weight from rear to 00:10:16.000 --> 00:10:18.000 front will remain the same. 00:10:18.001 --> 00:10:23.001 In this mathematical model of behavior and automobile, we can use a computer to 00:10:23.001 --> 00:10:25.001 simulate what would happen in actual practice. 00:10:27.000 --> 00:10:31.000 We have actually found that our mathematical model's automobile traffic predict 00:10:31.000 --> 00:10:33.001 very well many of the effects which we observe. 00:10:35.000 --> 00:10:39.000 Returning to our more general remarks about the use of computers, we first used 00:10:39.000 --> 00:10:43.001 computers to simulate situations in engineering, situation which 00:10:43.001 --> 00:10:45.000 we had been doing before by hand. 00:10:45.001 --> 00:10:49.001 The computer has allowed us to do much larger and more complex problems. 00:10:50.001 --> 00:10:54.000 But this ignored the order of magnitude effect which we spoke of. 00:10:55.001 --> 00:10:59.000 We are now beginning to use the machines in entirely new ways 00:10:59.000 --> 00:11:00.001 and entirely different problems. 00:11:01.000 --> 00:11:02.001 This is the exciting part. 00:11:03.000 --> 00:11:08.000 This is the intellectual aspect of applying the machines to completely new ideas 00:11:08.000 --> 00:11:10.000 that are so exciting to many people in the field. 00:11:11.000 --> 00:11:16.001 One of the characteristics of human beings is that among other things that they 00:11:16.001 --> 00:11:18.001 do is that they solve problems. 00:11:20.001 --> 00:11:26.000 And what it means, of course, to solve a problem is being able to not only get an 00:11:26.000 --> 00:11:33.000 answer to a question that arises in a particular situation, but then to 00:11:33.000 --> 00:11:39.001 find other cases that are similar to the initial one so that we are in effect in 00:11:39.001 --> 00:11:45.000 a position to solve not just one concrete problem, but a whole class of them. 00:11:45.000 --> 00:11:48.001 This is Professor Ernest Nagel, a leading logician and philosopher 00:11:48.001 --> 00:11:50.001 from Columbia University. 00:11:50.001 --> 00:11:57.000 Once a domain has been developed to the point where answers can 00:11:57.000 --> 00:12:03.000 be given from given set of assumptions 00:12:03.000 --> 00:12:09.001 simply by following some set of 00:12:09.001 --> 00:12:16.001 instructions or some rules, then it's not entirely evident that one 00:12:16.001 --> 00:12:21.001 should be thinking of the significance of every step that one is performing. 00:12:22.001 --> 00:12:25.001 Well, is it also possible to instruct the machines 00:12:25.001 --> 00:12:27.001 to follow the rules of thought? 00:12:27.001 --> 00:12:32.001 Indeed, I think this is, of course, the basis for having 00:12:32.001 --> 00:12:39.000 machines or computers since their entire task 00:12:39.000 --> 00:12:45.001 consists in following a set of rules or programs 00:12:46.001 --> 00:12:53.000 so that in a very short 00:12:53.000 --> 00:12:59.001 span of time they're able to come out with an answer that would have taken 00:12:59.001 --> 00:13:04.001 human beings an extraordinary length of time to produce. 00:13:05.000 --> 00:13:09.000 It seems to me that the computers, because they were able to ask new questions, 00:13:09.001 --> 00:13:12.000 also were able to get entirely new answers. 00:13:12.001 --> 00:13:16.001 They do not answer all the old questions, but because the questions are new, the 00:13:16.001 --> 00:13:18.001 answers are also new and very exciting. 00:13:20.000 --> 00:13:24.000 There is a strong tendency to speak of the machine as solving the problem, when 00:13:24.000 --> 00:13:27.001 in fact really it is the program which describes to the 00:13:27.001 --> 00:13:29.000 machine what the machine is to do. 00:13:30.000 --> 00:13:33.001 This is overlooked, and I think a great deal of confusion arises from this. 00:13:34.000 --> 00:13:37.001 It is not that we do not have adequate machines to solve our problems many times, 00:13:37.001 --> 00:13:41.000 but rather we lack adequate descriptions of how to solve the problem. 00:13:41.001 --> 00:13:46.001 This is a very important point to understand. As we spread out and learn more and 00:13:46.001 --> 00:13:51.001 more about our techniques of solving problems, we will be able to do 00:13:51.001 --> 00:13:53.000 wire and wire class of problems. 00:13:53.000 --> 00:13:57.000 It is not the machine so much as it is our lack of ideas, its controls.